8,266,100

2² × 5² × 131 × 631

Starting at 8,266,100, the Collatz iteration reaches 1 after 199 steps. The first transition is 4133050; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 131 × 631

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 18,103,008

Proper Divisor Sum 9,836,908

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #8266099 ← → #8266109

Radix Representation

Decimal	8266100
Binary	11111100010000101110100 (23 bits)
Octal	0o37420564
Hexadecimal	0x7E2174

Divisor Catalog (36)

1 2 4 5 10 20 25 50 100 131 262 524 631 655 1,262 1,310 2,524 2,620 3,155 3,275 6,310 6,550 12,620 13,100 15,775 31,550 63,100 82,661 165,322 330,644 413,305 826,610 1,653,220 2,066,525 4,133,050 8,266,100

Collatz Trajectory (199 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

8,266,100 4,133,050 2,066,525 6,199,576 3,099,788 1,549,894 774,947 2,324,842 1,162,421 3,487,264 1,743,632 871,816 435,908 217,954 108,977 326,932 163,466 81,733 245,200 122,600 61,300 30,650 15,325 45,976 22,988 11,494 5,747 17,242 8,621 25,864 12,932 6,466 3,233 9,700 4,850 2,425 7,276 3,638 1,819 5,458 2,729 8,188 4,094 2,047 6,142 3,071 9,214 4,607 13,822 6,911 20,734 10,367 31,102 15,551 46,654 23,327 69,982 34,991 104,974 52,487

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